A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three

On a compact three-dimensional Riemannian manifold with boundary, we prove the compactness of the full set of conformal metrics with positive constant scalar curvature and constant mean curvature on the boundary. This involves a blow-up analysis of a Yamabe equation with critical Sobolev exponents both in the interior and on the boundary.Comment: 27 pages. Comments are welcome!. arXiv admin note: text overlap with arXiv:1807.0840

MD-Manifold: A Medical Distance Based Manifold Learning Approach for Heart Failure Readmission Prediction

Dimension reduction is considered as a necessary technique in Electronic Healthcare Records (EHR) data processing. However, no existing work addresses both of the two points: 1) generating low-dimensional representations for each patient visit; and 2) taking advantage of the well-organized medical concept structure as the domain knowledge. Hence, we propose a new framework to generate low-dimensional representations for medical data records by combining the concept-structure based distance with manifold learning. To demonstrate the efficacy, we generated low-dimensional representations for hospital visits of heart failure patients, which was further used for a 30-day readmission prediction. The experiments showed a great potential of the proposed representations (AUC = 60.7%) that has comparative predictive power of the state-of-the-art methods, including one hot encoding representations (AUC = 60.1%) and PCA representations (AUC = 58.3%), with much less training time (improved by 99%). The proposed framework can also be generalized to various healthcare-related prediction tasks, such as mortality prediction

A priori estimates for anti-symmetric solutions to a fractional Laplacian equation in a bounded domain

In this paper, we obtain a priori estimates for the set of anti-symmetric solutions to a fractional Laplacian equation in a bounded domain using a blowing-up and rescaling argument. In order to establish a contradiction to possible blow-ups, we apply a certain variation of the moving planes method in order to prove a monotonicity result for the limit equation after rescaling

ICU Outcome Predictions Using Real-Time Signals with Wavelet-Transform-based Convolutional Neural Network

Intensive care units (ICUs) serve patients with life-threatening conditions. The limited ICU resources cause severe economic and healthcare burdens worldwide. It is critical to conduct ICU outcome predictions at an early stage and promote efficient use of ICU resources. However, all the current prediction methods have limitations such as unsatisfactory accuracy and depending on resource-demanding laboratory tests or expert domain knowledge. In this research, we design a wavelet-transformed-based convolutional neural network, WTCNN, which only requires patients’ vital sign series and information at ICU admission for real-time ICU outcome predictions. The model is evaluated using a large real-world ICU database and outperforms state-of-art baselines on both ICU mortality and length-of-stay prediction tasks. We conduct LIME for model interpretation and prescriptive analysis. Our work provides an efficient tool for ICU outcome predictions, allowing healthcare providers to take action promptly on patients at risk and reduce the negative impacts on patient outcomes

ICU Outcome Predictions Using Real-Time Signals with Wavelet-Transform-based Convolutional Neural Network

Intensive care units (ICUs) serve patients with life-threatening conditions. The limited ICU resources cause severe economic and healthcare burdens worldwide. It is critical to conduct ICU outcome predictions at an early stage and promote efficient use of ICU resources. However, all the current prediction methods have limitations such as unsatisfactory accuracy and depending on resource-demanding laboratory tests or expert domain knowledge. In this research, we design a wavelet-transformed-based convolutional neural network, WTCNN, which only requires patients’ vital sign series and information at ICU admission for real-time ICU outcome predictions. The model is evaluated using a large real-world ICU database and outperforms state-of-art baselines on both ICU mortality and length-of-stay prediction tasks. We conduct LIME for model interpretation and prescriptive analysis. Our work provides an efficient tool for ICU outcome predictions, allowing healthcare providers to take action promptly on patients at risk and reduce the negative impacts on patient outcomes

Covariance localization in the ensemble transform Kalman filter based on an augmented ensemble

With the increased density of available observation data, data assimilation has become an increasingly important tool in marine research. However, the success of the ensemble Kalman filter is highly dependent on the size of the ensemble. A small ensemble used in data assimilation could cause filter divergence, undersampling and spurious correlations. The primary method to alleviate these problems is localization. It can eliminate some spurious correlations and increase the rank of the forecast error covariance matrix. The ensemble transform Kalman filter has been widely used in various studies as a deterministic filter. Unfortunately, the covariance localization cannot be directly applied to ensemble transform Kalman filter. The new covariance localization needs to be presented to adapt the ensemble transform Kalman filter. Based on the method of expanded ensemble and eigenvalue decomposition, this study describes a variation of covariance localization that takes advantage of an unbiased covariance matrix from the expanded ensemble. Experiments described herein show that the new method outperforms the localization methods proposed by others when used in the ensemble transform Kalman filter. The new method yields an analysis estimate that is closer to the true state under different experimental conditions

Multi-views Fusion CNN for Left Ventricular Volumes Estimation on Cardiac MR Images

Left ventricular (LV) volumes estimation is a critical procedure for cardiac disease diagnosis. The objective of this paper is to address direct LV volumes prediction task. Methods: In this paper, we propose a direct volumes prediction method based on the end-to-end deep convolutional neural networks (CNN). We study the end-to-end LV volumes prediction method in items of the data preprocessing, networks structure, and multi-views fusion strategy. The main contributions of this paper are the following aspects. First, we propose a new data preprocessing method on cardiac magnetic resonance (CMR). Second, we propose a new networks structure for end-to-end LV volumes estimation. Third, we explore the representational capacity of different slices, and propose a fusion strategy to improve the prediction accuracy. Results: The evaluation results show that the proposed method outperforms other state-of-the-art LV volumes estimation methods on the open accessible benchmark datasets. The clinical indexes derived from the predicted volumes agree well with the ground truth (EDV: R2=0.974, RMSE=9.6ml; ESV: R2=0.976, RMSE=7.1ml; EF: R2=0.828, RMSE =4.71%). Conclusion: Experimental results prove that the proposed method may be useful for LV volumes prediction task. Significance: The proposed method not only has application potential for cardiac diseases screening for large-scale CMR data, but also can be extended to other medical image research fieldsComment: to appear on Transactions on Biomedical Engineerin

Timely ICU Outcome Prediction Utilizing Stochastic Signal Analysis and Machine Learning Techniques with Readily Available Vital Sign Data

The ICU is a specialized hospital department that offers critical care to patients at high risk. The massive burden of ICU-requiring care requires accurate and timely ICU outcome predictions for alleviating the economic and healthcare burdens imposed by critical care needs. Existing research faces challenges such as feature extraction difficulties, low accuracy, and resource-intensive features. Some studies have explored deep learning models that utilize raw clinical inputs. However, these models are considered non-interpretable black boxes, which prevents their wide application. The objective of the study is to develop a new method using stochastic signal analysis and machine learning techniques to effectively extract features with strong predictive power from ICU patients' real-time time series of vital signs for accurate and timely ICU outcome prediction. The results show the proposed method extracted meaningful features and outperforms baseline methods, including APACHE IV (AUC = 0.750), deep learning-based models (AUC = 0.732, 0.712, 0.698, 0.722), and statistical feature classification methods (AUC = 0.765) by a large margin (AUC = 0.869). The proposed method has clinical, management, and administrative implications since it enables healthcare professionals to identify deviations from prognostications timely and accurately and, therefore, to conduct proper interventions.This is a manuscript of the article Published as S. Wang, Y. Jiang, Q. Li and W. Zhang, "Timely ICU Outcome Prediction Utilizing Stochastic Signal Analysis and Machine Learning Techniques with Readily Available Vital Sign Data," in IEEE Journal of Biomedical and Health Informatics. doi: https://doi.org/10.1109/JBHI.2024.3416039. © 2024 IEEE. Posted with Permission